(i) Absorption, spontaneous emission, and stimulated emission.

(ii) The possible fates of a quantum of energy adsorbed by a molecule. These can be divided into four categories, emission of the energy from the same molecule, energy transfer to another molecule followed by emission, and either reaction of the starting molecule or of one to which the energy has been transferred.

(iii) Emission processes from the molecule itself: Fluorescence, phosphorescence, internal conversion, intersystem crossing and their measurement. The meaning of quantum yield and how it is determined. Discussion of the factors that influence the quantum yields of the different processes.

(iv) Measurement of fluorescence decay (see fluorescence decay from a pyrene solution)

(v) Simple discussion of electronic energy transfer and means for following it. Fluorescence quenching and the Stern-Volmer equation.

Use lecture notes and Wayne & Wayne, *Photochemistry*
for particular topics.

There are two relevant experiments, one on the dissociation energy of I_{
2} and the other on fluorescence and fluorescence quenching.

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**1.** For a 3.7 x 10^{-3} M solution of naphthalene
in hexane the peak of the first absorption band is at 301 nm. The intensity
of light at this wavelength is reduced to 0.1 of its orginal value on passing
through 1 cm of this solution. Obtain the molar absorption coefficient.

**2.** The molar absorption coefficient for a compound is 3 x 10^{
4} dm^{3} mol^{-1}
cm^{-1} at 313 nm, where the compound is photochemically
bleached. The product does not absorb at 313 nm. A 1.5 x 10^{
-3} M solution of the compound in a 1 cm^{3}
cell of 1 cm^{2} cross section was placed in the
path of a light beam of 0.01 mW cm^{-2} at 313 nm.
The absorbance decreased by 7 % of its original value in two hours. Obtain
the quantum yield of the bleaching reaction.

**3.** In a solution of K_{3}[Fe(C_{
2}O_{4})_{3}
] the Fe(III) is reduced to Fe(II) on exposure to light. The quantum
yield for Fe(II) formation at λ = 400 nm is 1.13 and the molar extinction
coefficient (base *e*) at this wavelength is 594 cm^{ -1}
mol^{-1} dm^{ 3} . A solution
of concentration 0.006 mol dm^{ -3} is contained
in a cell of thickness 1 mm. The solution is irradiated for 20 min with
light of λ = 400 nm and it is found that 3.4 x 10^{-6}
of Fe(II) are formed. What is the intensity of light incident on the cell
(measured in quanta s^{ -1} )?

Light from a line of a mercury lamp is totally absorbed in a
solution of potassium ferrioxalate, which decomposes with a quantum efficiency
of unity at a rate of 10^{-7} mol s^{-1}
. When the same light is used to investigate the fluorescence of a solution
of Y in a cell 1 cm thick, the following results are found:

[Y]/mol dm^{-3} |
0.1 | 0.01 | 0.001 |

Total emitted intensity/quanta s^{-1} |
2.4 x 10^{16} |
2.4 x 10^{16} |
1.5 x 10^{16} |

Find values for the quantum efficiency of fluorescence of Y and the extinction
coefficient of Y. When [Y] is 0.01 mol dm^{3} addition
of chloride ion has the following effect:

[Cl^{-}]/mol dm^{-3} |
0 | 0.01 | 0.1 |

Total emitted intensity/quanta s^{-1} |
2.4 x 10^{16} |
1.2 x 10^{16} |
2.16 x 10^{15} |

Comment on these values.

The processes involved in the photochemical dimerization of an anthracene derivative in solution in ethanol are summarized below:

Give expressions for the quantum yields of the different processes in terms of the rate constants.

When the concentration of A is reduced to a level such that the quantum
yields for dimerization and quenching are negligible, the fluorescence quantum
yield is 0.218 and the intensity of fluorescence *I* expressed in
arbitrary units, falls with time as follows:

I |
0.97 | 0.62 | 0.40 |

t/ns |
2 | 4 | 6 |

Calculate the rate constants *k*_{F} and *
k*_{NR}.

At higher concentrations of A the quantum yield for dimerization Φ_{
D} varies with concentration of A as follows:

F_{D} |
0.037 | 0.081 | 0.105 | 0.121 | 0.137 |

[A]/mol dm^{-3} |
0.01 | 0.03 | 0.05 | 0.07 | 0.1 |

Calculate the remaining rate constants *k*_{D}
and *k*_{Q}. Comment on their values.

**6.** Propanone absorbs 313 nm radiation and exhibits a weak blue emission
(380 - 470 nm) from a triplet state with a lifetime τ of 2 x 10^{
-4} s. Biacetyl does not absorb at 313 nm, but strongly quenches
this triplet emission. Calculate the rate coefficient for this quenching
process from the data below.

Φ_{P}/Φ_{Q} |
1.21 | 1.43 | 1.65 | 1.84 | 2.02 |

[Biacetyl]/mol dm^{-3} |
0.006 | 0.012 | 0.018 | 0.023 | 0.028 |

Φ_{P} and Φ_{Q} are the
quantum yields for phosphorescence in the absence and presence of biacetyl.

Naphthalene contained in an alcohol-ether low temperature glass
absorbs light at λ = 315 nm and two different emission spectra are observed.
The quantum yields and lifetimes for the two emissions are (i) Φ = 0.3,
τ = 3 x 10^{-7} s, and (ii) Φ =0.03, τ = 2.3. Estimate
as many kinetic parameters as you can for the various processes occurring,
assuming that no internal conversion or physical quenching occur. Explain
qualitatively the magnitudes of the quantities that you obtain.

**8.** Show that the quantum yield Φ_{ F}
, the radiative lifetime τ_{ F} and the observed
lifetime τ in fluorescence are related by the equation

Φ_{F} = τ/Φ_{
F}

where τ = 1/(*k*_{F} + *k*_{
NR}) and *k*_{F} is the radiative
rate constant and *k*_{NR} is the sum of
rate constants for non-radiative processes depopulating the excited state.
Quenching may be assumed to be absent.

When the fullerene C_{70}, dissolved in a solid
rare gas at 20 K is exposed to ultraviolet light, two distinct bands are
seen. One has its origin at 15520 cm^{-1} and is approximately
10 times more intense than the second, whose origin is at 12588 cm^{
-1}. The lifetime of the stronger emission is 600 ps and
its fluorescence quantum yield is 10^{-4} . The lifetime
of the weaker emission is 50 ms. Identify the types of state involved in
the emission processes and the transitions between them. Estimate the radiative
lifetime for the stronger emission and comment on its value.

Indicate how values of the rate constants for other radiative and non-radiative processes in this system might be obtained.

**9.** (a) Explain why there is often a mirror image relationship between
the absorption and fluorescence spectra of a molecule in solution. Under
what conditions would such symmetry *not* be expected?

(b) A molecule is excited from its ground state to an excited singlet state
in a flash photolysis experiment. Give expressions for the quantum yields
of fluorescence Φ_{F} and phosphorescence Φ_{
P} in terms of the rate constants for fluorescence *k*_{
F} , phosphorescence *k*_{P}
, and singlet-triplet intersystem crossing *k*_{ISC}
.

Hence show that the rate constant for the disappearance of the excited
singlet state is equal to *k*_{F}/Φ_{
F}.

Assuming no chemical reactions take place, discuss the processes that could
cause the sum of the two quantum yields (Φ_{ F}
+ Φ_{P} to be smaller than the result obtained
above.

(c) Continuous light (1.0 x 10^{16} quanta s^{
-1} falls on a cell of thickness 1.0 mm containing a solution
of a fluorescent compound B. The total fluorescence was determined as a
function of the concentration of B.

[B]/mol dm^{-3} |
0.0030 | 0.030 | 0.300 |

Fluorescence/10^{15} quanta s^{
-1} |
2.00 | 3.40 | 3.40 |

Determine the molar absorption (extinction) coefficient and the fluorescence quantum yield of B. Note that the fluorescence intensities at the two higher concentrations are identical.